A Maxwell Like Formulation of Gravitational Theory in Minkowski Spacetime

Abstract

In this paper using the Clifford bundle formalism a Lagrangian theory of the Yang-Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski spacetime is presented. It is shown how two simple hypothesis permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory the field equations are shown to be equivalent to Einstein's equations.

This is a version of a paper published in Int. J. Mod. Phs. D 16(6), 1027-1041 (2007) where some misprints and typos have been corrected, some references have been updated, a footnote has been added and some few sentences have been rewritten to better explain the role of the (plastic) deformation tensor h

References in corpus (5)

• Gravitational Energy-Momentum Density in Teleparallel Gravity
• On a class of invariant coframe operators with application to gravity
• An Ambiguous Statement Called 'Tetrad Postulate' and the Correct Field Equations Satisfied by the Tetrad Fields
• The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential
• A class of quasi-linear equations in coframe gravity

Cited by in corpus (7)

• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Hamiltonian formulation of a simple theory of the teleparallel geometry
• The Effective Lorentzian and Teleparallel Spacetimes Generated by a Free Electromagnetic Field
• Reply to Itin, Obukhov and Hehl paper "An Electric Charge has no Screw Sense - A Comment on the Twist-Free Formulation of Electrodynamics by da Rocha & Rodrigues"
• Pair and Impar, Even and Odd Form Fields and Electromagnetism
• Some Thoughts on Geometries and on the Nature of the Gravitational Field
• Notoph-Graviton-Photon Coupling